Wow... this is extremely anti-business. I don't think you understand that offering a service puts you in a situation of both liability and obligation. As it is, you don't technically have an obligation to do more than is provided for in your terms; however, the reality is that, in order to be successful, you need to do whatever your customers require within the sphere of services and offerings that can be expected based on your claims and advertisement.
Requiring businesses to provide their products or services to absolutely anyone -- and continue doing so even when a user has clearly violated the spirit of service or product usage (because in this scenario there would be little or no value to any kind of terms of use) -- means taking away any means any business would otherwise have of protecting its revenue stream in reasonable ways.
Freedom of speech on private forums... now you're coming across as either a troll (successful) or a kid who's gotten banned for posting too much porn/hate speech/insulting mods too many times.
Anyway, there are good reasons that governments shouldn't restrict a business' ability to choose not to do business with entities as they wish.
Federal case law protects the rights of people to refuse service based on protecting business interests. LegalZoom has a nice blog post on it [0]. Unruh Civil Rights Law does prevent arbitrary discrimination though.
If you owned a retail store, and someone came in every day yelling and screaming and breaking things, would you say they should have the right to do so, since the store is open to the public?
Why? If you really feel strongly that this is practical and everything should be allowed, you can go ahead and offer your own Nazis-and-pedophiles-welcome streaming service. I don't see why others should have their freedom of association revoked just because of your personal whims.
I'm fairly anti-business as a rule, but this goes a bit too far for me. There does exist a right to refuse service and it is a legitimate, if very gray-area, right. There do exist multiple fora for political speech, though I'm not sure if that's what you meant by "public speech".
What you're asking for is, in my mind, a pretty clear violation of the right to assembly which includes the right to not associate.
It should be illegal for companies to refuse service to anyone or offer them worse terms that someone they never did business with.
Even more generally, it should be illegal to ban users from any service, and censor public speech in any way, even on private forums.